Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“The supreme, the merciless, the destroyer of opposition, the exalted King, the shepherd, the protector of the quarters of the world, the King the word of whose mouth destroys mountains and seas, who by his lordly attack has forced mighty and merciless Kings from the rising of the sun to the setting of the same to acknowledge one supremacy.”
—Ashurnasirpal II (r. 883–59 B.C.)
“The trees stand in the setting sun,
I in their freckled shade
Regard the cavalcade of sin,
Remorse for foolish action done,
That pass like ghosts regardless, in
A human image made....”
—Philip Larkin (1922–1986)
““Oh, let’s go up the hill and scare ourselves,
As reckless as the best of them tonight,
By setting fire to all the brush we piled
With pitchy hands to wait for rain or snow....””
—Robert Frost (1874–1963)